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## 'Days and Dates' printed from http://nrich.maths.org/

If today is Monday we know that in 702 days time (that is in 100
weeks and 2 days time) it will be Wednesday. This is an example of
"clock" or "modular" arithmetic.

What day will it be in 15 days? 26 days? 234 days?

In 2, 9, 16 and 23 days from now, it will be a Wednesday. What
other numbers of days from now will be Wednesdays? Can you
generalise what you have noticed?

Choose a pair of numbers and find the remainders when you divide
by 7. Find the remainder when you divide the total by 7. For
example

$15 \div 7 = 2$ remainder $1$

$26 \div 7 = 3$ remainder $5$

$15 + 26 = 41$

$41 \div 7 = 5$ remainder $6$

Try some more numbers. What do you notice about the remainders?
Can you justify what you see?

Now find the remainder when you divide the product of 15 and 26
by 7. What happens? Can you justify what you see? Try some more
numbers.

How can I use these ideas to work out what day my birthday
will be on next year?